Higgs criticality of Dirac spin liquids on depleted triangular lattices

Abstract

We investigate Higgs criticality in candidate U(1) Dirac spin liquids across a family of depleted triangular lattices: the triangular, kagome, and maple-leaf geometries. For each, we identify the symmetry-allowed spinon-pairing channel connecting the U(1) state to a proximate ${\mathbb{Z}}_2$ spin liquid, deriving the corresponding quantum electrodynamics (QED${}_3$)-Higgs theory. While the triangular and kagome lattices share a low-energy description with $N_f=4$ Dirac fermions, the maple-leaf lattice yields an analogous theory with $N_f=12$ and a distinct nodal structure where the Dirac cones can move along high-symmetry lines in momentum space instead of gapping out. Using a large-$N_{f,b}$ expansion, we compute critical exponents and the scaling dimensions of the symmetry-allowed Yukawa couplings. Although Higgs-field fluctuations and a large fermion flavor number strongly suppress the Yukawa coupling---pushing the maple-leaf lattice closer to stability than its counterparts---we find that the coupling remains relevant at leading order in all three cases, substantially reducing its scaling dimension on the maple-leaf lattice and asymptotically breaking Lorentz and conformal invariance. Ultimately, our results provide a unified framework demonstrating how the interplay between fermion flavor count and nodal geometry dictates the fate of the QED${}_3$-Higgs transition.

arXiv comment18 pages, 11 figures, 2 tables